A Lindenstrauss theorem for some classes of multilinear mappings

被引：3

作者：

Carando, Daniel ^{[1
]}

Lassalle, Silvia ^{[2
]}

Mazzitelli, Martin ^{[1
]}

机构：

[1] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat Pab 1, RA-1428 Buenos Aires, DF, Argentina

[2] Univ San Andres, Dept Matemat, Buenos Aires, DF, Argentina

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 427卷 / 01期

关键词：

Integral formula; Norm attaining multilinear mappings and polynomials; Lindenstrauss-type theorems; PHELPS-BOLLOBAS PROPERTY; NORM; POLYNOMIALS; OPERATORS; IDEALS; SPACES; FORMS;

D O I：

10.1016/j.jmaa.2014.11.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Under some natural hypotheses, we show that if a multilinear mapping belongs to some Banach multilinear ideal, then it can be approximated by multilinear mappings belonging to the same ideal all whose Arens extensions attain their norms at the same point. We prove a similar result for the class of symmetric multilinear mappings. We see that the quantitative (Bollobas-type) version of these results fails in every multilinear ideal. (C) 2014 Published by Elsevier Inc.

引用

页码：248 / 262

页数：15

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